We argue that in at least a portion of the history of the universe the relic
background neutrinos are spatially-extended, coherent superpositions of mass
states. We show that an appropriate quantum mechanical treatment affects the
neutrino mass values derived from cosmological data. The coherence scale of
these neutrino flavor wavepackets can be an appreciable fraction of the causal
horizon size, raising the possibility of spacetime curvature-induced
decoherence.

I am quite intrigued at this paper. Basically, if I understand correctly:

a) if the lightest mass eigenstate is very light then quantum coherence (ie. neutrinos created in flavour eigenstate and staying there) can have significant effects on the total neutrino energy density.

b) if you look at their plot no. 2, then am I correct to understand that the correction on the total neutrino energy density is 10% and so we have about 10−4 correction to closure of the universe, which could be detectable in the next 10 years?

c) nobody has put this into CAMB (and it should be some work but not supermuch).

d) neutrinos can, in principle, decohere gravitationally (do we understand this at all?) and so the effect might not be there and the standard codes are fine and dandy.

This did look interesting. Not sure I understand it though: who calculates the density using Eq 7? As far as I know Cosmics, CMBFAST, CAMB and CMBEASY all use mass eigenstates, as in Eq 8, which seems to be what the paper is advocating.

Any why should neutrinos stay in flavour eigenstates when they don't in neutrino oscillation experiments?

(note m terms in Eqs. 2 and 4 can be dropped to high accuracy because the neutrinos were very relativistic at decoupling)

My understanding of the neutrino oscillation result is that it has to do with the local nature of the observation. Picturesquely, you can say that the differing propagation speeds of the mass eigenstates lead to a situation where the blend of mass eigenstates is locally that you'd expect for a different flavor.

This is I think at the root of the remark about gravitational decoherence. When the difference in position of the different mass eigenstates becomes of order the size of a galaxy, you might start to wonder if *someone* is going to notice.

[This is I think a slightly separate mechanism from the oscillation we see on Earth, where the particles are all near-relativistic; for the terrestrial 1 MeV observation it's phase interference, but for the 1 meV galaxy case it is actually literally that the centers of the two wavepackets are sufficiently displaced.]

What is actually the main upshot of the paper? The first thing seems to be the influence of the chemical potential for the different species (they call this the degeneracy parameter), which influences what happens when you emerge from Tweak. I would guess this is something you compute from particle physics – and I guess is already in codes?

The other issue is that you could compute the neutrino mass density naively; the solution is don't be naive (and the various codes, as Anthony tells us, aren't.)

The idea of having some gravitational decoherence effect is fun, but I am not sure if it is observable by the cosmological expansion. If the mechanism is that wavepackets for the different eigenstates are separated by a large amount, it seems to me that "observations" (human or mystical-gravitational) would reproduce the original statistics implicit in the wavefunction amplitude. So instead of gravitating wavepackets, you have gravitating particles; on average, however, both locally and globally, the total energy is the same.

So, do we agree that the first line of equation (8) is correct for both neutrinos in flavour eigenstates and those in the mass eigenstates? So the codes that we have now are actually ok and there is nothing really new here...

BTW, I thought that the party line was the neutrinos are in flavour eigenstate when they are created, but that they fall into a mass eigenstate after scattering... In other words, neutrinos weren't created and then travelled to us, but instead scattered until the epoch of the last neutrino scattering). But they seem to oppose this picture, right?

Eq. 8 looks right for both mass (first line) and flavor (second line)!

Let me ask a basic question: what is the relevance of quantum coherence?

As far as I can tell, the only observable difference is in the influence of the chemical potential of the various species. It leads to a funny initial distribution of species that would not be what you'd expect as someone doing a homework problem ("there are three particles with masses m1, m2, m3; they decouple at T; what are their relative abundances.")

I don't know how to calculate the chemical potential, but that indeed might perhaps be where quantum coherence effects come in.

However, once that distribution is fixed, well below Tweak it doesn't matter if it is achieved by a bunch of flavor eigenstate neutrinos or a bunch of mass eigenstate neutrinos (with the population distribution you would expect given the prior flavor distribution.) A quantum mechanical expectation value gets replaced by a statistical average.

"Neutrinos are produced in flavor eigenstates but then propagate as mass eigenstates. Therefore, the simple notion of a neutrino with fixed mass having its own last scattering surface is a bit too naive."

(The use of the word "propagate" here does not necessarily mean "the wavefunction collapses to a mass eigenstate and then the particle propagates along like that". One could test quantum coherence with the Teradollar experiment of building a WMAP for neutrinos, and watching the relative amplitudes of the different flavors oscillate depending on position relative to the LSS.)

Dude, I looked into numbers once about direct dection of neutrino background and it is depressing... Not 103 depressing but over 1010 depressing.
The issue with these neutrinos is that they are so very cold; try converting 1.9K to eV and then compare this with numbers neutrino physicists are tossing around when talking about detectors...